Arnd Scheel
University of Minnesota
Diffusive synchronization of oscillations

I will discuss properties of temporal oscillations in reaction-diffusion systems posed on R^n. The main result shows that localized perturbations to initial conditions decay diffusively. Techniques involve an ODE normal form, linear diffusive estimates, and maximal regularity for a quasilinear system. I will also discuss temporal asymptotics of bounded perturbations and conclude with some open problems concerned with the description of solutions which are pointwise close to oscillations. This is joint work with Thierry Gallay (U Grenoble).